You operate a plant that manufactures steel dumpsters. Your plant receives large rectangular metal sheets and then removes four equal squares from each corner. Finally, the remaining four tabs are bent upward 90 degrees where their edges are welded together. The result in a rectangular steel box with an open top (5 faces) You have two options from your supplier for metal sheet sizes: 4 x 4 meters 4 x 8 meters The steel sheets cost $20/m The supplier will buy back the corner scraps for an 80% refund. A customer has requested an order of dumpsters (all the same size) that can hold a total of 1000m of material. You must determine how to fill the order in the most cost-efficient manner. Suggested approach: 1. Choose a sheet size and determine an expression for the volume of the dumpster for corner- square side- length x. 2. Determine an expression for the number of those dumpsters required to fill the 1000m order. Determine an expression for the scrap material for those dumpsters. 4. Determine an expression for the cost of the dumpsters and an expression for the 80% refund on scraps. 5. Determine an equation for the total cost associated with a corner-square length x, and find the value of x that will minimize cost. 6. Repeat this process for the other sheet size. 7. Summarize your results in a conclusion paragraph and explain how you would fill the order in the most cost-efficient way possible